It is generally agreed that two key points always attract special concerns during the modelling of anomaly-based intrusion detection. One is the techniques about discerning two classes with different features, another is the construction/selection of the observed sample of normally occurring patterns for system normality characterization. In this paper, instead of focusing on the design of specific anomaly detection models, we restrict our attention to the analysis of the anomaly detector’s operating environments, which facilitates us to insight into anomaly detectors’ operational capabilities, including their detection coverage and blind spots, and thus to evaluate them in convincing manners. Taking the similarity with the induction problem as the starting point, we cast anomaly detection in a statistical framework, which gives a formal analysis of anomaly detector’s anticipated behavior from a high level. Some existing problems and possible solutions about the normality char...